Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7tc)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a7tc.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, -(1/4)}, z] == (1/(523309248 z^(5/2))) ((-20675655 + 20675655 E^(4 Sqrt[z]) - 41351310 Sqrt[z] - 41351310 E^(4 Sqrt[z]) Sqrt[z] - 7518420 z + 7518420 E^(4 Sqrt[z]) z + 40098240 z^(3/2) + 40098240 E^(4 Sqrt[z]) z^(3/2) - 57283200 z^2 + 57283200 E^(4 Sqrt[z]) z^2 + 78921216 z^(5/2) + 78921216 E^(4 Sqrt[z]) z^(5/2) - 147667968 z^3 + 147667968 E^(4 Sqrt[z]) z^3 + 715751424 z^(7/2) + 715751424 E^(4 Sqrt[z]) z^(7/2) + 50177664 z^4 - 50177664 E^(4 Sqrt[z]) z^4 - 208740864 z^(9/2) - 208740864 E^(4 Sqrt[z]) z^(9/2) - 2789376 z^5 + 2789376 E^(4 Sqrt[z]) z^5 + 11255808 z^(11/2) + 11255808 E^(4 Sqrt[z]) z^(11/2) + 32768 z^6 - 32768 E^(4 Sqrt[z]) z^6 - 131072 z^(13/2) - 131072 E^(4 Sqrt[z]) z^(13/2) - 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-23468211 + 6587568 z - 352512 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-23468211 + 6587568 z - 352512 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]